Download Induced emf - Engineering Physics - Lecture Slides and more Slides Engineering Physics in PDF only on Docsity!
Today’s agenda:
Induced emf. You must understand how changing magnetic flux can induce an emf, and be able to determine the direction of the induced emf.
Faraday’s Law. You must be able to use Faraday’s Law to calculate the emf induced in a circuit.
Lenz’s Law. You must be able to use Lenz’s Law to determine the direction induced current, and therefore induced emf.
Generators. You must understand how generators work, and use Faraday’s Law to calculate numerical values of parameters associated with generators.
Back emf. You must be able to use Lenz’s law to explain back emf.
Induced emf and Faraday’s Law
Magnetic Induction
We have found that an electric current can give rise to a magnetic field…
I wonder if a magnetic field can somehow give rise to an electric current…
Note that ―change‖ may or may not not require observable (to you) motion.
A magnet may move through a loop of wire
N S
move magnet toward coil
v (^) region of magnetic field change area of loop inside magnetic field
N S
rotate coil in magnetic field
this part of the loop isclosest to your eyes
A magnet may move through a loop of wire, or a loop of wire may be moved through a magnetic field. These involve observable motion.
I
I^ B
A changing current in a loop of wire
In the this case, nothing observable (to your eye) is moving, although, of course microscopically, electrons are in motion.
Induced emf is produced by a changing magnetic flux.
changing I
changing B
induced I
A changing current in a loop of wire gives rise to a changing magnetic field (predicted by Ampere’s law)
A changing current in a loop of wire gives rise to a changing magnetic field (predicted by Ampere’s law) which can induce a current in another nearby loop of wire.
We can quantify the induced emf described qualitatively in the last few slides by using magnetic flux.
Experimentally, if the flux through N loops of wire changes by dB in a time dt, the induced emf is
dB = - N. dt
Faraday’s law of induction is one of the fundamental laws of electricity and magnetism.
I wonder why the – sign…
Faraday’s Law of Magnetic Induction
Your text, pages 997-998, shows how to determine the direction of the induced emf. Argh! Lenz’s Law, coming soon, is much easier.
εaverage = - N (^) t^ B.
This is sometimes shown as another expression of Faraday’s Law:
dB = - N , dt
B
d E ds = - dt
is the magnetic flux.
Faraday’s Law of Magnetic Induction
B B dA
Web pagehttp://sol.sci.uop.edu/~jfalward/electromagneticinduction/electromagneticinduction.html with pictures of a whole bunch of applications (dead spring 2013):
We’ll use this version in a ―later‖ lecture.
In the equation
Possible homework hint: B d B B dA B(t) dA if B varies but loop B.
Ways to induce an emf:
change B
change the area of the loop in the field
Possible homework hint: for a circular loop, C=2R, so A=r^2 =(C/2)^2 =C^2 /4, so you can express d(BA)/dt in terms of dC/dt.
Possible Homework Hint.
I
The magnetic field is not uniform through the square loop, so you can’t use BA to calculate the flux. Take an infinitesimally thin strip. Then the flux is d = BdAstrip. Integrate from a to b to get the flux through the strip.
a
b
Today’s agenda:
Induced emf. You must understand how changing magnetic flux can induce an emf, and be able to determine the direction of the induced emf.
Faraday’s Law. You must be able to use Faraday’s Law to calculate the emf induced in a circuit.
Lenz’s Law. You must be able to use Lenz’s Law to determine the direction induced current, and therefore induced emf.
Generators. You must understand how generators work, and use Faraday’s Law to calculate numerical values of parameters associated with generators.
Back emf. You must be able to use Lenz’s law to explain back emf.
Lenz’s law—An induced emf always gives rise to a current whose magnetic field opposes the change in flux.*
Experimentally…
*Think of the current resulting from the induced emf as ―trying‖ to maintain the status quo— to prevent change.
I N^ S
v
- (^) - If Lenz’s law were not true—if there were a + sign in Faraday’s law—then a changing magnetic field would produce a current, which would further increase the magnetic field, further increasing the current, making the magnetic field still bigger…
(counterclockwise) (clockwise)
Rotating the coil about the vertical diameter by pulling the left side toward the reader and pushing the right side away from the reader in a magnetic field that points from right to left in the plane of the page.
(counterclockwise)
Today’s agenda:
Induced emf. You must understand how changing magnetic flux can induce an emf, and be able to determine the direction of the induced emf.
Faraday’s Law. You must be able to use Faraday’s Law to calculate the emf induced in a circuit.
Lenz’s Law. You must be able to use Lenz’s Law to determine the direction induced current, and therefore induced emf.
Generators. You must understand how generators work, and use Faraday’s Law to calculate numerical values of parameters associated with generators.
Back emf. You must be able to use Lenz’s law to explain back emf.
Motional emf: an overview
An emf is induced in a conductor moving in a magnetic field.
Your text introduces four ways of producing motional emf.
B
d = - dt
side view
B
A
- Flux change through a conducting loop produces an emf: rotating loop.
ε = NBA sin (^) t
I = NBAR^ ^ sin (^) t P = INBA sin (^) t
start with this
derive these
